2y(y+5)=18

Simple and best practice solution for 2y(y+5)=18 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 2y(y+5)=18 equation: 


Simplifying
2y(y + 5) = 18

Reorder the terms:
2y(5 + y) = 18
(5 * 2y + y * 2y) = 18
(10y + 2y2) = 18

Solving
10y + 2y2 = 18

Solving for variable 'y'.

Reorder the terms:
-18 + 10y + 2y2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 10y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 5y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 5y + y2)' equal to zero and attempt to solve:

Simplifying
-9 + 5y + y2 = 0

Solving
-9 + 5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 5y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + 5y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5y + y2 = 0 + 9
5y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
5y + y2 = 9

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 9 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 9 + 6.25

Combine like terms: 9 + 6.25 = 15.25
6.25 + 5y + y2 = 15.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(y + 2.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
y + 2.5 = 3.905124838

Simplifying
y + 2.5 = 3.905124838

Reorder the terms:
2.5 + y = 3.905124838

Solving
2.5 + y = 3.905124838

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 3.905124838 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 3.905124838 + -2.5
y = 3.905124838 + -2.5

Combine like terms: 3.905124838 + -2.5 = 1.405124838
y = 1.405124838

Simplifying
y = 1.405124838


Subproblem 2
y + 2.5 = -3.905124838

Simplifying
y + 2.5 = -3.905124838

Reorder the terms:
2.5 + y = -3.905124838

Solving
2.5 + y = -3.905124838

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -3.905124838 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -3.905124838 + -2.5
y = -3.905124838 + -2.5

Combine like terms: -3.905124838 + -2.5 = -6.405124838
y = -6.405124838

Simplifying
y = -6.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.405124838, -6.405124838}
Solution
y = {1.405124838, -6.405124838}

See similar equations:

| 5x-3+6x=2x+4-4x | | x^3-.5x^2-4x+2=0 | | 4(x-5)-5=6x+4.4-4x | | 2w+8=18 | | -6n+48=-8n+40 | | 16n^2-114=14 | | 2log(3)x-log(3)64=0 | | 15.2y=136.8 | | 9x+27=4(x+8) | | 2log(3)x=log(3)64 | | d(x)=12-0.04x | | ln(x)=4.9+ln(6.8) | | 24=(n*7)-(n*3) | | 5(U+2)-8V=-2 | | t=30+5h | | 4m-2=3m+4 | | 6=3(W-2)-6W | | y=27+7x | | y=7x+27 | | 9(x+4)-(2x-1)=1 | | ln(x)=0.32 | | 20x^2+10x+5=0 | | 5=1+1.3ln(x+1) | | -16+32n=-40+8n | | 6y+50=700 | | 41=2x-11 | | 15x^2-5x+7=0 | | b=37.72+-1.5c | | 2/2+2/x-2/3x= | | 2/2+2/x-2/3x=2/7 | | (x-3)6 = (x+6)7 | | 2/2+2/x-2/3=2/7 |

Equations solver categories